Finiteness properties of generalized local cohomology modules for minimax modules

Cogent Mathematics

Sh. Payrovi¹  Z. Rahimi-Molaei¹  I. Khalili-Gorji¹ 

[1] Imam Khomeini International University;

关键词: generalized local cohomology;    minimax module;   

DOI  :  10.1080/23311835.2017.1327683

来源: DOAJ

【 摘 要 】

Let R be a commutative Noetherian ring, I an ideal of R, M be a finitely generated R-module and t be a non-negative integer. In this paper, we introduce the concept of I, M-minimax R-modules. We show that $ \text{ Hom}_R(R/I,\, H^t_I(M,\, N)/K) $ is I,M-minimax, for all I,M-minimax submodules K of $ H^t_I(M,\, N) $, whenever N and $ H_{I}^{0}(M) $, $ H_{I}^{1}(M), \, \cdots , \, H_{I}^{t-1}(M) $ are I, M-minimax R-modules. As consequence, it is shown that $ \text{ Ass}_R H^t_I(M,\, N)/K $ is a finite set.

【 授权许可】

Unknown